SRC/cgelss.f(3)

NAME
SRC/cgelss.f

SYNOPSIS

  Functions/Subroutines
subroutine cgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, info)
CGELSS solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation

  subroutine cgelss (integer m, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) s, real rcond, integer rank, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

CGELSS solves overdetermined or underdetermined systems for GE matrices

Purpose:

    !>
    !> CGELSS computes the minimum norm solution to a complex linear
    !> least squares problem:
    !>
    !> Minimize 2-norm(| b - A*x |).
    !>
    !> using the singular value decomposition (SVD) of A. A is an M-by-N
    !> matrix which may be rank-deficient.
    !>
    !> Several right hand side vectors b and solution vectors x can be
    !> handled in a single call; they are stored as the columns of the
    !> M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
    !> X.
    !>
    !> The effective rank of A is determined by treating as zero those
    !> singular values which are less than RCOND times the largest singular
    !> value.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A. N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrices B and X. NRHS >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the first min(m,n) rows of A are overwritten with
    !>          its right singular vectors, stored rowwise.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,M).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the M-by-NRHS right hand side matrix B.
    !>          On exit, B is overwritten by the N-by-NRHS solution matrix X.
    !>          If m >= n and RANK = n, the residual sum-of-squares for
    !>          the solution in the i-th column is given by the sum of
    !>          squares of the modulus of elements n+1:m in that column.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,M,N).
    !>

    S

    !>          S is REAL array, dimension (min(M,N))
    !>          The singular values of A in decreasing order.
    !>          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
    !>

    RCOND

    !>          RCOND is REAL
    !>          RCOND is used to determine the effective rank of A.
    !>          Singular values S(i) <= RCOND*S(1) are treated as zero.
    !>          If RCOND < 0, machine precision is used instead.
    !>

    RANK

    !>          RANK is INTEGER
    !>          The effective rank of A, i.e., the number of singular values
    !>          which are greater than RCOND*S(1).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1, and also:
    !>          LWORK >=  2*min(M,N) + max(M,N,NRHS)
    !>          For good performance, LWORK should generally be larger.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is REAL array, dimension (5*min(M,N))
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  the algorithm for computing the SVD failed to converge;
    !>                if INFO = i, i off-diagonal elements of an intermediate
    !>                bidiagonal form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 176 of file cgelss.f.

Author

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